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Journal Articles Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences Year : 2017

A complete characterisation of All-versus-Nothing arguments for stabiliser states

Abstract

An important class of contextuality arguments in quantum foundations are the All-versus-Nothing (AvN) proofs, generalising a construction originally due to Mermin. We present a general formulation of All-versus-Nothing arguments, and a complete characterisation of all such arguments which arise from stabiliser states. We show that every AvN argument for an n-qubit stabiliser state can be reduced to an AvN proof for a three-qubit state which is local Clifford-equivalent to the tripartite GHZ state. This is achieved through a combinatorial characterisation of AvN arguments, the AvN triple Theorem, whose proof makes use of the theory of graph states. This result enables the development of a computational method to generate all the AvN arguments in Z2 on n-qubit stabiliser states. We also present new insights into the stabiliser formalism and its connections with logic.

Dates and versions

hal-01528687 , version 1 (29-05-2017)

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Samson Abramsky, Rui Soares Barbosa, Giovanni Carù, Simon Perdrix. A complete characterisation of All-versus-Nothing arguments for stabiliser states. Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences, 2017, Second quantum revolution: foundational questions, 375 (2106), ⟨10.1098/rsta.2016.0385⟩. ⟨hal-01528687⟩
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